The “barbell” portfolio has long been considered an investment strategy. Since his fame after the 2010 publication of the book *The Black Swan*, Nassim Nicholas Taleb has often been associated with the strategy. Recent research illustrates the critical connection between the barbell, core-satellite portfolios and safety-first financial planning – and how advisors can improve on using standard deviation as a measure of risk.

That research is in an article, “Tail Risk Constraints and Maximum Entropy,” that appeared in the journal *Entropy*, coauthored by Donald Geman, Hélyette Geman, and Taleb. Its thesis, approach and results are worth a closer look. The basic idea is to anchor a portfolio to a hard, downside-only risk constraint – i.e., not standard deviation – and then to split the portfolio into two elements that meet two very different objectives: a hedged element that strictly meets the downside risk constraint and an aggressive element in which you maximize the uncertainty of the result.

Don Geman was a fellow graduate student when I was a PhD student in the pure mathematics department at Northwestern University. We had not been in touch since graduate school. I had vaguely heard of his success as a mathematician, and that he was based at Johns Hopkins University and France’s École Normale Supérieure. What I was not aware of was that Don’s wife, Hélyette, also a distinguished mathematician, was the supervisor of Taleb’s PhD thesis.

**The basic idea of the barbell**

The basic idea of the barbell strategy is that the portfolio is divided into two parts: an extremely conservative portfolio for safety, and a highly speculative portfolio for extra rewards with extra risk. A strategy that has sometimes been placed in this category – though a bit of a bastardization – is the core-and-satellite strategy, in which the bulk of an equity market portfolio is placed in a passive index fund, or funds, while the smaller portion, the satellite, speculates in concentrated active funds or hedge funds.

In the Gemans and Taleb’s article, motivation is provided by their claim that the measure of risk in nearly all investment finance theory, standard deviation of return, is unsatisfactory because its minimization not only limits downside risk, but also curtails upside opportunity. Better, they say, to impose a risk-control criterion that only limits downside risk in a manner that accords with the specific risks that investors want to avoid.

The risk-control criterion that the authors choose is a combination of VaR and CVaR. VaR – “value at risk” – is the portfolio loss that could occur during a specified time period with a probability *p*. “For example,” says a CFA Institute publication, “a portfolio that is expected to lose no more than $1 million 95% of the time (or 19 of every 20 days) has a VaR of $1 million.”

Note that VaR tells you how *likely* it is that you will lose no more than $1 million, but it doesn’t tell you *how much more* than $1 million you might lose. VaR has been criticized for not providing this information. This is important, because if there is a 5% chance that $1 million will be lost during the next 20 days, but the loss will be due to a rogue trader, that loss could actually be $5 billion.

CVaR, or “conditional value at risk,” is meant to compensate for VaR’s missing information. CVaR is the expected loss *given* (i.e. conditional on) the fact that at least $1 million is lost. So if, for example, a portfolio has a VaR of $1 million at the 95% confidence level, but the 5% tail event consists of a loss of $5 billion, then CVaR is $5 billion, because the expected loss *given* that a loss greater than $1 million occurs is $5 billion.